For every torsion free Fuchsian group F with Poincaré’s -operator norm ║г║=1, it is proved that there exists an extremal Beltrami differential of F which is also extremal under its own boundary correspondence...For every torsion free Fuchsian group F with Poincaré’s -operator norm ║г║=1, it is proved that there exists an extremal Beltrami differential of F which is also extremal under its own boundary correspondence. It is also proved that the imbedding of the Teichmüller space T(Γ) into the universal Teichmüller space T is not a global isometry unless Γ is an elementary group.展开更多
Let R be a hyperbolic Riemann surface of conformal infinite type. Denote by A the Banach space of all integrable holomorphic quadratic differentials on R, and by B0 and B the predual and dual of A, respectively. This ...Let R be a hyperbolic Riemann surface of conformal infinite type. Denote by A the Banach space of all integrable holomorphic quadratic differentials on R, and by B0 and B the predual and dual of A, respectively. This paper gives a complete description of the convexity of these three spaces.展开更多
文摘For every torsion free Fuchsian group F with Poincaré’s -operator norm ║г║=1, it is proved that there exists an extremal Beltrami differential of F which is also extremal under its own boundary correspondence. It is also proved that the imbedding of the Teichmüller space T(Γ) into the universal Teichmüller space T is not a global isometry unless Γ is an elementary group.
基金Project supported by the National Natural Science Foundation of China (No.19701024).
文摘Let R be a hyperbolic Riemann surface of conformal infinite type. Denote by A the Banach space of all integrable holomorphic quadratic differentials on R, and by B0 and B the predual and dual of A, respectively. This paper gives a complete description of the convexity of these three spaces.
